Without using a calculator find the greatest prime factor of 156−76
[7 + b]^6 - 7^6
b^6 + 42 b^5 + 735 b^4 + 6860 b^3 + 36015 b^2 + 100842 b + 117649 -7^6
Sub 8 for b
262,144 + 1,376,256 + 3,010,560 + 3,512,320 + 2,304,960 + 806,736
11,272,976 = 2^4 * 11 * 13^2 * 379
15^6 - 7^6 = {factor using difference/sum of cubes}
(15 - 7)(15^2 + 15*7 + 7^2)(15 + 7) (15^2 - 15*7 + 49) =
(15 - 7) (15+7)(15^2 - 15*7 + 49)(15^2 + 15*7 + 49) =
(8)(22)(169)(379)
(2^3)(2*11)(13* 13)(379)
(2^4)(11)(13^2)(379) is the largest prime factor
A typo of 139 should be 169.
Thanks, guest.....correction made !!!
